Just for the fun of it I took a condition where three balloons were positioned in a straight line at equal increments.

The time required for two balloons to touch is the same as the time required for three balloons to touch. ( This was done with a thought experiment.)

When three objects of equal mass are located similarly to the balloons and are allowed to fall together by gravitational attraction. The time required for the three objects to touch is larger then two objects.

The time for three objects to touch is
T = ln( 3/2 x M x G ).

The time for two objects to touch is
T = ln ( M x G )

M equals the mass of one of the objects

G is the gravitational constant.

I assumed the initial size of the objects were relatively small compared to the initial distance between the objects.

This is not to say that this error canít be compensated for with some additions to your theory but some modification are necessary if this theory is to explain known experimental evidence.